Fitting effective diffusion models to data associated with a "glassy" potential: Estimation, classical inference procedures, and some heuristics
Fitting effective diffusion models to data associated with a "glassy" potential: Estimation, classical inference procedures, and some heuristics
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DOI：
10.1137/050643647
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发表时间：
2007-01-01
影响因子：
1.6
通讯作者：
Calderon, Christopher P.
中科院分区：
文献类型：
--
作者：
Calderon, Christopher P.
许多研究人员利用原子模拟产生的数据成功地获得了低维扩散模型的参数。这就提出了有关有效估计、拟合优度检验和置信区间估计的各种问题。长时间序列数据和与假设的过程模型相关的转变密度的知识对于获得上述问题的答案有很大帮助。不幸的是，很少有过渡密度的封闭式表达式。使用近似的转变密度进行估计和推断（主要兴趣在于 Ait-Sahalia 的转变密度展开如何在各种多尺度环境中执行）。还提出了一种用于估计非线性扩散的启发式策略，该策略不需要假设扩散系数的精确函数形式。本研究的最后部分探讨了如何利用上述发现来帮助构建通过某种类型的均质化实现的扩散近似。
A variety of researchers have successfully obtained the parameters of low-dimensional diffusion models using the data that results from atomistic simulations. This raises a variety of questions about effcient estimation, goodness-of-fit tests, and confidence interval estimation. Long time series data and knowledge of the transition density associated with the assumed process model can be of great assistance in obtaining answers to the aforementioned questions. Unfortunately, a closed-form expression for the transition density is rarely available. Estimation and inference are carried out using approximated transition densities ( the primary interest is in how Ait-Sahalia's transition density expansions perform in various multiscale contexts). A heuristic strategy for estimating a nonlinear diffusion which does not require one to assume the exact functional form of the diffusion coefficients is also presented. The final part of this study explores how the above findings can be used to help construct a diffusion approximation made possible through a type of homogenization.